Indeterminate equation

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An indeterminate equation, in mathematics, is an equation for which there is an infinite set of solutions; for example, 2x = y is a simple indeterminate equation. A diophantine equation is an indeterminate equation in which both the solution and the terms must be integers. Indeterminate equations cannot be directly solved from the given information. For example, the equations

$\ ax + by = c$

$\ x^2 - Py^2 = 1$

where a, b, c, and P are given integers (provided that P is not a square number), are indeterminate equations. In general, we are interested in finding integer solutions to these equations. Equations of the first form are called Diophantine equations. Those of the second form are named Pell's equations.